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ORIGINAL PAPER
Systemic exposure following intravitreal administration of therapeuticagents: an integrated pharmacokinetic approach. 1. THR-149
Marc Vanhove1 • Bernard Noppen1 • Jean-Marc Wagner2 • Tine Van Bergen1 • Philippe Barbeaux1 •
Alan W. Stitt1,3
Received: 9 March 2021 / Accepted: 24 June 2021 / Published online: 23 July 2021� The Author(s) 2021
AbstractIntravitreal (IVT) injection of pharmacological agents is an established and widely used procedure for the treatment of
many posterior segment of the eye diseases. IVT injections permit drugs to reach high concentrations in the retina whilst
limiting systemic exposure. Beyond the risk of secondary complications such as intraocular infection, the potential of
systemic adverse events cannot be neglected. Therefore, a detailed understanding of the rules governing systemic exposure
following IVT drug administration remains a prerequisite for the evaluation and development of new pharmacological
agents intended for eye delivery. We present here a novel mathematical model to describe and predict circulating drug
levels following IVT in the rabbit eye, a species which is widely used for drug delivery, pharmacokinetic, and pharma-
codynamic studies. The mathematical expression was derived from a pharmacokinetic model that assumes the existence of
a compartment between the vitreous humor compartment itself and the systemic compartment. We show that the model
accurately describes circulating levels of THR-149, a plasma kallikrein inhibitor in development for the treatment of
diabetic macular edema. We hypothesize that the model based on the rabbit eye has broader relevance to the human eye
and can be used to analyze systemic exposure of a variety of drugs delivered in the eye.
Keywords Intravitreal administration � Systemic exposure � Integrated pharmacokinetics
Introduction
In recent years, intravitreal (IVT) injection has become the
preferred administration route of pharmacological agents
for the treatment of the back of the eye diseases such as
age-related macular degeneration and diabetic retinopathy.
Despite being invasive and associated with a low risk of
rhegmatogenous retinal detachment [1], the procedure
offers the advantage to immediately achieve high, thera-
peutically-effective drug levels in the vitreous chamber [2].
Localized IVT administration also serves to considerably
limit overall systemic exposure and therefore potential
systemic adverse events [2]. This, however, doesn’t imply
that the risk of systemic complications doesn’t exist for
drugs administered intravitreally. Indeed, the systemic risk
is well illustrated by the commonly used anti-VEGF agents
which IVT administration is suspected to be associated
with increased risk for ischemic cerebrovascular disease,
thromboembolic events, non-ocular hemorrhagic events,
nephrotoxicity, acute blood pressure elevations, serious
systemic infections, gastrointestinal disorders, and even
mortality. This is a low but consistent risk and limiting the
bioavailability of systemic VEGF could be detrimental for
vascular integrity, especially in patients with retinal disease
who are also at risk for cardiovascular diseases [3–7].
Therefore, accurate understanding of systemic exposure
following ocular delivery remains a critical step in the
development of new ophthalmological drugs. Attempts to
model e.g. drug circulating levels after IVT administration
remain sporadic, though, and evaluation of systemic
exposure, whether for preclinical models or human data, is
This article is a companion paper of ‘‘https://doi.org/10.1007/
s10928-021-09774-9’’.
& Marc Vanhove
marc.vanhove@oxurion.com
1 Oxurion N.V., Gaston Geenslaan 1, 3001 Leuven, Belgium
2 Haute Ecole de la Province de Liege, Avenue Montesquieu 6,
4101 Seraing, Belgium
3 Centre for Experimental Medicine, Queen’s University
Belfast, Belfast, Northern Ireland, UK
123
Journal of Pharmacokinetics and Pharmacodynamics (2021) 48:825–836https://doi.org/10.1007/s10928-021-09773-w(0123456789().,-volV)(0123456789().,-volV)
oftentimes restricted to analyses based solely on descrip-
tive parameters such as maximum observed concentration
(Cmax), time to reach Cmax (tmax), and area under the curve
(AUC) [8–15]. There are, however, noticeable exceptions.
Le et al. [16] described an integrated ocular-systemic
model for the anti-factor D antigen-binding fragment (Fab)
lampalizumab in the cynomolgus monkey which takes into
account target mediated drug disposition, target turnover,
and drug distribution across ocular tissues and systemic
circulation. Also, Luu et al. [17] reported a model for the
anti-VEGF DARPin abicipar pegol that incorporates VEGF
binding kinetics, VEGF expression levels, and VEGF
turnover rates to describe ocular and systemic pharma-
cokinetic data in the rabbit. Buitrago et al. [18] used a
three-compartment pharmacokinetic model to assess
plasma levels after IVT injection of the chemotherapy drug
topotecan in rabbits. Gadkar et al. [19] proposed a math-
ematical model for ocular (including vitreous, aqueous
humor, and retina) and systemic pharmacokinetic analysis
of a variety of antibodies and antibody fragments that can
be generalized for all protein fragments derived from an
antibody regardless of the presence of an Fc region.
Finally, Xu et al. [20] and Zhang et al. [21] have shown
that serum concentration of the anti-VEGF Fab fragment
ranibizumab after IVT administration in patients with
retinal vein occlusion, diabetic macular edema, and age-
related macular degeneration can be described by a one-
compartment model with first-order absorption into and
first-order elimination from the systemic circulation.
THR-149, a bicyclic peptide identified by a combination
of phage-based selections and directed medicinal chemistry
(see Teufel et al. [22] for a general description of the
method), is a potent and specific inhibitor of plasma kal-
likrein currently being developed by Oxurion N.V. for the
treatment of diabetic macular edema (source: www.clin
icaltrials.gov). Here, we report the pharmacokinetic prop-
erties of THR-149 in the rabbit and propose a novel
mathematical model to describe systemic exposure, in the
form of circulating drug levels, following IVT adminis-
tration. In the current study, the proposed mathematical
expression was derived from a pharmacokinetic model that
assumes the existence of an additional compartment
between the vitreous humor (VH) compartment itself (i.e.
the compartment where the drug is administered) and the
systemic compartment. We also hypothesize, here and in
our accompanying paper (Vanhove et al., this issue of J.
Pharmacokinet. Pharmacodyn. https://doi.org/10.1007/
s10928-021-09774-9), that this kind of model is generally
applicable to describe plasma levels of drugs delivered into
the eye.
Methods
Animal studies
Housing and all experimental procedures were conducted
according to accepted best practice (EU Directive/AAA-
LAC or similar) and approved by Institutional Animal Care
and Research Advisory Committee of the KU Leuven
according to the 2010/63/EU Directive. All animal proce-
dures were also performed in accordance with the ARVO
Statement for the Use of Animals in Ophthalmic and
Vision Research.
Nonlinear regression analyses
Nonlinear regression analyses were performed using the
GraphPad Prism software ver. 5.02 (GraphPad Software
Inc., La Jolla, CA) applying, unless otherwise stated, equal
weighting (i.e. performing minimization based on absolute
distances squared). For the modelling of plasma levels
following IVT administration with Eq. 13 (Fig. 5b), and in
order to compute a unique value for the parameter k2, the
data set was analyzed ‘‘globally’’ i.e. considering that the
data obtained for the different doses represent a unique set
of data, and with k2 used as a ‘‘shared’’ parameter to
employ the terminology used in GraphPad Prism (we refer
the reader to the GraphPad Prism software ver. 5.02 user’s
manual for a description of how global fitting of such data
sets can be performed). Precision on the fitted parameters
was expressed as 95% confidence intervals (CI95%).
Intravitreal pharmacokinetics
Male New-Zealand White (NZW) rabbits (10 weeks old,
1.7–2.0 kg) received a single injection of 50 lL of 2.5 mg/
mL THR-149 (125 lg) in each eye. General anesthesia was
induced by intramuscular injection of 50 mg/mL ketamin
(Ketalar, Pfizer) and 2% (v/v) sedative (Rompun, Bayer
Health Care). Pupils were dilated with a drop of tropi-
camide (Tropicol, Thea Pharma). IVT injections were
performed using 30G, 0.3 mL insulin syringes with half-
unit (50 lL) marks (BD Micro-Fine) under 4 mg/mL
topical anesthesia (Unicain, Thea Pharma). The animals
were sacrificed 1 h, 4 h, 8 h, 24 h, 48 h, 96 h, and 168 h
after injection (3 animals per time point), the injected eyes
were enucleated and the vitreous was collected. The vit-
reous samples from each eye were treated separately,
homogenized mechanically, and clarified by centrifugation
as previously described [23], then further clarified by
0.2 lm filtration (Nanosep� MF with Bio-Inert� mem-
brane, VWR, cat. 516-8554). THR-149 was quantified in
the vitreous samples by HPLC. HPLC analyses were
826 Journal of Pharmacokinetics and Pharmacodynamics (2021) 48:825–836
123
performed using an Acquity UPLC instrument (Waters).
One volume of each sample was diluted into 1.5 volume of
8.33% (v/v) acetonitrile, 0.17% (v/v) trifluoroacetic acid
(TFA), 0.067% (v/v) Tween-20, and 6 lL of the diluted
samples were injected on a BEH300 C18 1.7 lm,
2.1 9 100 mm Acquity UPLC column (Waters, cat.
186003686) pre-equilibrated in 0.1% (v/v) TFA. Elution
was performed by applying a 1-mL, 5–40% (v/v) acetoni-
trile linear gradient in 0.1% (v/v) TFA and THR-149 was
detected by following the absorbance at 215 nm. The flow
rate was 100 lL/min and the temperature of the column
was maintained at 75 �C. The concentration of THR-149 in
the samples was calculated by integration of the relevant
peak and reference to a standard curve obtained by injec-
tion of a series of samples of known concentration.
Data (THR-149 concentration vs. time) were analyzed
based on a mono-compartmental model (Eq. 1, where D is
the dose, VD,VH the vitreal volume of distribution, and k1
the first-order rate constant of vitreal drug elimination)
applying a proportional weighting i.e. performing mini-
mization based on relative distances squared. Half-life in
the VH was calculated from Eq. 2 and vitreal clearance
(CLVH) was obtained from Eq. 3.
½THR � 149�VH ¼ D
VD;VH� e�k1�t ð1Þ
t1=2 ¼ lnð2Þk1
ð2Þ
CLVH ¼ k1 � VD;VH ð3Þ
Intravenous pharmacokinetics
NZW rabbits (n = 8, males and females, 12 weeks old,
1.7–2.0 kg, Charles River) received a single intravenous
administration of THR-149 (5 mg/kg) via the marginal ear
vein using a 26G needle (Becton Dickinson) under local
anesthesia (10% xylocaine spray). Blood was collected via
the marginal ear vein in EDTA-coated sample tubes
(Sarstedt, Multivette�, MUL-E-600) connected to a 26G
needle 30 min, 2 h, and 4 h after THR-149 administration
for the first four animals, and 1 h, 3 h, and 6 h after THR-
149 administration for the remaining four animals. Plasma
was prepared by centrifugation (10 min at 14009g) and
THR-149 levels were determined by LC–MS using an
Acquity UPLC coupled to a QDa instrument (Waters).
Prior to analysis, plasma samples were diluted with 2 or 3
volumes of 0.1% (v/v) formic acid in acetonitrile and
centrifuged for 10 min at 13,000 rpm. The supernatants
were further diluted in 0.1% (v/v) formic acid in water and
6 lL of the diluted samples were injected on a BEH C18
300A, 1.7 lm, 2.1 9 100 mm Acquity UPLC column
(Waters, cat. 186003686) pre-equilibrated in 10% (v/v)
acetonitrile and 0.1% (v/v) formic acid. The temperature of
the column was maintained at 65 �C. Elution was per-
formed by applying a 3-mL, 10–44% (v/v) acetonitrile
linear gradient in 0.1% (v/v) formic acid at a flow rate of
600 lL/min. THR-149 was detected in positive polarity
single ion recording mode via its [M?3H]3? ion. The
concentration of THR-149 in the samples was calculated
by integration of the peak in the ion chromatogram and
reference to a standard curve obtained by injection of a
series of samples of known concentration (625–4.88 ng/
mL).
Data (plasma concentration vs. time) were analyzed
based on a mono-compartmental model using Eqs. 4, 5 and
6 (with D the dose, VD,syst the systemic volume of distri-
bution, k3 the first-order rate constant of systemic drug
elimination, and CLsyst the systemic clearance) applying a
proportional weighting.
½THR � 149�syst ¼D
VD;syst� e�k3�t ð4Þ
t1=2 ¼ lnð2Þk3
ð5Þ
CLsyst ¼ k3 � VD;syst ð6Þ
Plasma levels following intravitrealadministration
THR-149 was solubilized at 2.5, 5.0, 7.5, 10, and 20 mg/
mL. Male NZW rabbits (14–16 weeks old, average weight
3.1 kg, CEGAF) received a single, 50-lL IVT adminis-
tration of THR-149 in both eyes, thus representing a dose
of 0.125 mg, 0.25 mg, 0.375 mg, 0.5 mg or 1 mg per eye,
depending on the concentration of the administered solu-
tion. The administration procedure was identical to the one
described above except that 29G syringes were used. Blood
samples were collected 0.5, 1, 4, 8, and 24 h after THR-149
administration via the marginal ear vein in EDTA-coated
sample tubes (Sarstedt, Multivette�, MUL-E-600) con-
nected to a 26G needle and plasma was prepared by cen-
trifugation (10 min at 14009g). THR-149 concentration in
plasma samples was assessed by LC–MS/MS at Charles
River Discovery (Groningen, The Netherlands). Of each
prepared sample, a 30-lL aliquot was injected onto the
HPLC column by an automated sample injector (SIL20-AC
HT, Shimadzu, Japan). Chromatographic separation was
performed on a reversed phase analytical column (Atlantis
T3, 150 9 2.1 mm, 3.0 lm, Waters, USA) held at a tem-
perature of 30 �C. Components were separated using a
gradient of acetonitrile containing 0.1% (v/v) formic acid
in ultrapurified H2O containing 0.1% (v/v) formic acid at a
flow rate of 0.2 mL/min. The MS analyses were performed
using an API 5000 MS/MS system equipped with a Turbo
Journal of Pharmacokinetics and Pharmacodynamics (2021) 48:825–836 827
123
Ion Spray interface (both from Sciex, USA). The instru-
ment was operated in multiple-reaction-monitoring mode.
The acquisitions were performed in positive ionization
mode with optimized settings for THR-149. Data were
acquired and processed using the AnalystTM data system (v
1.4.2, Sciex, USA).
Data (THR-149 concentration vs. time) were analyzed
based on Eqs. 7 or 13 (see ‘Results’ section).
Results
Intravitreal pharmacokinetics
Pharmacokinetic data following administration of 125 lg
of THR-149 in the rabbit eye are shown in Fig. 1 and
summarized in Table 1. THR-149 exhibited a relatively
long residence time in the VH with a first-order rate con-
stant of vitreal elimination (k1) of 0.0195 h-1 corre-
sponding to a half-life of 36 h. The vitreal volume of
distribution was slightly larger than the vitreous volume
(1.66 mL vs. 1.15 mL) and vitreal clearance was
0.032 mL/h. Of note, there was no evidence of metabolic
degradation of THR-149 in the vitreous (not shown).
Intravenous pharmacokinetics
The decrease in the circulating concentration of THR-149
following intravenous administration in rabbit (5 mg/kg)
was best described by a single exponential (Fig. 2). Plasma
concentration vs. time data were thus analyzed based on a
mono-compartmental model (Eqs. 4, 5 and 6) leading to a
first-order rate constant of systemic elimination (k3) of
0.64 h-1 (corresponding to a half-life of 1.1 h), a volume
of distribution of 0.51 L/kg, and a clearance of 5.5 mL/
min/kg (Table 1). Together with a high metabolic stability
in presence of liver microsomes which suggests a limited
potential of hepatic clearance (not shown), these data are in
agreement with renal clearance at glomerular filtration rate.
Plasma levels following intravitrealadministration
Systemic exposure (i.e. plasma levels over time) following
IVT administration of THR-149 in rabbit was measured for
doses ranging from 0.125 mg per eye to 1 mg per eye
(corresponding to total doses per animal ranging from 0.25
to 2 mg since THR-149 was administered bilaterally—drug
elimination from each eye was assumed to be identical and
additive when modeling plasma exposure). These data are
Fig. 1 Pharmacokinetics in the rabbit VH following intravitreal
administration of 125 lg of THR-149. Data are shown as mean ±
SD. The solid line represents the best fit given by Eq. 1. THR-149
exhibits a relatively long residence time in the VH with a rate
constant of drug elimination (k1) of 0.0195 h-1 corresponding to a
half-life of 36 h
Table 1 Pharmacokinetic parameters of THR-149 in rabbit
Parameter
Vitreous volume (mL) 1.15
k1 (h-1) 0.0195 [0.0177–0.0214]
Vitreal half-life (h) 36 [32–39]
VD,VH (mL) 1.66 [1.46–1.92]
CLVH (mL/min) 0.032 [0.029–0.036]
k2 (h-1) 0.056 [0.049–0.063]
k3 (h-1) 0.64 [0.55–0.73]
Systemic half-life (h) 1.1 [0.9–1.2]
VD,syst (L/kg) 0.51 [0.40–0.73]
CLsyst (mL/min/kg) 5.5 [4.4–6.5]
The values of k1 and k3 were obtained from intravitreal pharma-
cokinetics (Fig. 1) and intravenous pharmacokinetics (Fig. 3),
respectively. The value of k2 was calculated from plasma levels fol-
lowing IVT administration
0 2 4 60.01
0.1
1
10
100
Time (h)
noitartnecnoc941-
RHT
) Lm/gµ(
Fig. 2 Drug plasma levels following intravenous administration of
5 mg/kg of THR-149 in rabbits. Data are shown as mean ± SD and
were analyzed based on a mono-compartmental model. The solid line
represents the best fit given by Eq. 4. THR-149 is cleared quickly
from the circulation with a rate constant of drug elimination (k3) of
0.64 h-1 corresponding to a half-life of 1.1 h
828 Journal of Pharmacokinetics and Pharmacodynamics (2021) 48:825–836
123
presented in Fig. 3a. Plasma levels increased steadily, the
higher levels being observed at the latest time point (24 h)
for all doses. Overall plasma levels were also directly
proportional to actual dosing as shown from the perfect
correlation between the area under the curve (AUC) mea-
sured between 0 and 24 h by the trapezoidal method and
the dose (Fig. 3b).
Xu et al. and Zhang et al. [20, 21] have modelled cir-
culating drug levels following IVT administration on the
basis of a model with first-order absorption into and first-
order elimination from the systemic circulation, a model
which, therefore, is essentially identical to the two-com-
partment pharmacokinetic model depicted in Fig. 4a. In
this model, k1 represents the first-order rate constant for
transfer of the drug from the vitreal compartment to the
systemic compartment and k3 the first-order rate constant
for systemic elimination. Although neither Xu et al. nor
Zhang et al. present an analytical solution to their model,
the variation of the drug concentration in each of these
compartments as a function of time can be obtained by
solving (i.e. integrating) the following system of linear
differential equations (Eq. syst. 1), where A and B
represent the VH and systemic compartments, respectively,
and C the eliminated drug (Fig. 4a):
dA=dt ¼ �k1 � AdB=dt ¼ k1 � A� k3 � BdC=dt ¼ k3 � B
ðsyst:1Þ
The solution of such a system of linear differential
equations is common knowledge. For the second com-
partment, representing systemic distribution, the solution is
in the form of Eq. 7 where [THR-149]syst represents the
concentration of the drug in plasma at any point in time
(see e.g. [24]):
½THR � 149�syst ¼D � k1
VD;syst � k1 � k3ð Þ � e�k3�t � e�k1�t� �
ð7Þ
The rate constants k1 and k3 in Eq. 7 also appear in
Eqs. 1 and 4, respectively, and therefore the value of all the
parameters of Eq. 7 (namely D, VD,syst, k1, and k3) are
known from either intravitreal or intravenous pharma-
cokinetics. Equation 7 should thus accurately predict drug
circulating levels following IVT administration. Figure 5a
shows, however, that this is not the case. Equation 7 indeed
not only poorly describes actual drug levels in general, but
it also predicts that the circulating concentration will reach
a maximum value (Cmax) at * 5.6 h whereas THR-149
levels are observed to increase steadily for at least 24 h.
We, therefore, asked whether the data could be better
represented on the basis of a three-compartment pharma-
cokinetic model (Fig. 4b) that includes, compared to the
model used above (Fig. 4a), an extra compartment that we
will refer to here as the ‘‘ocular tissues compartment’’ and
which represents a compartment through which the drug
transits when being drained from the vitreous into the
systemic compartment. In this model, k2 represents the
Fig. 3 Plasma levels (a) and systemic exposure expressed as area
under the curve (AUC) between 0 and 24 h obtained by the
trapezoidal method (b) following bilateral intravitreal administration
of THR-149 in rabbit. Data in a are shown as mean ± SD. Doses
ranged from 0.125 to 1 mg per eye (corresponding to total doses per
animal ranging from 0.25 to 2 mg)
Fig. 4 Two-compartment (a) and three-compartment (b) pharmacoki-
netic models used to analyze drug circulating levels following
intravitreal administration of THR-149 in rabbit
Journal of Pharmacokinetics and Pharmacodynamics (2021) 48:825–836 829
123
first-order rate constant for transfer of the drug from the
ocular tissues compartment to the systemic compartment.
Similarly to Eq. syst. 1, the variation of the drug con-
centration in each compartment as a function of time can
be obtained from the following system of linear differential
equations (Eq. syst. 2) where A, B, and C represent the VH,
ocular tissues, and systemic compartments, respectively,
and D the eliminated drug (Fig. 4b):
dA=dt ¼ �k1 � AdB=dt ¼ k1 � A� k2 � BdC=dt
dD=dt
¼¼
k2 � B� k3 � Ck3 � C
ðsyst:2Þ
Solving/integrating this system of differential equations
is, however, significantly more complex and the solutions
have, to our knowledge, never been reported. We propose a
methodology to tackle this problem in the ‘Appendix’
section of this manuscript which leads, after final re-ar-
rangement, to the following analytical solution (Eqs. 8, 9,
10, 11):
At ¼ A0 � e�k1�t ð8Þ
Bt ¼A0 � k1
k2 � k1ð Þ � e�k1�t � e�k2�t� �ð9Þ
Ct ¼A0 � k1 � k2
k1 � k2ð Þ � 1
k1 � k3
� e�k1�t þ 1
k3 � k2
� e�k2�t�
þ k1 � k2
k1 � k3ð Þ � k2 � k3ð Þ � e�k3�t
� ð10Þ
Dt ¼ A0 �
k2 � k3
k2 � k1ð Þ � k1 � k3ð Þ � e�k1�t þ k1 � k3
k1 � k2ð Þ � k2 � k3ð Þ � e�k2�t
þ k1 � k2 � k2 � k1ð Þk1 � k2ð Þ � k1 � k3ð Þ � k2 � k3ð Þ � e
�k3�t
þ k2 � k3 � k2 � k3ð Þ � k1 � k3 � k1 � k3ð Þ þ k1 � k2 � k1 � k2ð Þk1 � k2ð Þ � k1 � k3ð Þ � k2 � k3ð Þ
0
BBBBBBB@
1
CCCCCCCA
ð11Þ
In each compartment, the drug concentration depends on
the dose and the volume of distribution of that compart-
ment. Applying this reasoning to the two compartments
that can be experimentally sampled, i.e. the VH and the
systemic compartment (via collection of plasma), Eqs. 8
and 10 can be re-written into Eqs. 12 and 13 by substituting
D/VD for A0.
THR � 149½ �VH¼D
VD;VH� e�k1�t ð12Þ
THR�149½ �syst¼D � k1 � k2
VD;syst � k1 � k2ð Þ
� 1
k1 � k3
� e�k1�tþ 1
k3 � k2
� e�k2�tþ k1 � k2
k1 � k3ð Þ � k2 � k3ð Þ � e�k3�t
� �
ð13Þ
Following a similar reasoning as above, Eq. 13 can thus
be used to model or analyze plasma concentration data
following IVT administration. This equation, however, is
relatively complex and robust determination of all indi-
vidual parameters from a given set of experimental data
may be challenging. Our approach was, therefore, to ‘‘ed-
ucate’’ this model with the information obtained from
intravitreal and intravenous pharmacokinetics, as illus-
trated in Fig. 6, by attributing a fixed value to the
Fig. 5 Plasma levels following bilateral intravitreal administration of
THR-149 in rabbit. Data are shown as mean ± SD. Doses varied
between 0.125 and 1 mg per eye (corresponding to total doses per
animal ranging from 0.25 to 2 mg). Data were analyzed based either
(a) on a two-compartment pharmacokinetic model (Fig. 4a) using
Eq. 7, or (b) on a three-compartment pharmacokinetic model
(Fig. 4b) using Eq. 13. The values of k1 and k3 in Eqs. 7 and 13
were fixed to those obtained from intravitreal and intravenous
pharmacokinetics, respectively, i.e. 0.0195 h-1 and 0.64 h-1. The
solid lines for (b) represent the best fit given by Eq. 13 with k2 set as
the only variable parameter
830 Journal of Pharmacokinetics and Pharmacodynamics (2021) 48:825–836
123
parameters VD,syst, k1, and k3, thus leaving k2 as the sole
variable parameter. Analysis of experimental data with this
methodology are shown in Fig. 5b. It is immediately
apparent that Eq. 13 allows a much better prediction of the
experimental data than Eq. 7 while remaining perfectly
coherent with intravitreal and intravenous pharmacokinetic
data. In addition, having ‘‘educated’’ Eq. 13 with intravit-
real and intravenous pharmacokinetic data, the value for k2
can be extracted with very good precision (here 0.056 h-1
with a 95% confidence interval of 0.049–0.063—see also
Table 1) despite the complexity of the model.
Finally, the analytical solution of Eq. syst. 2 in the form
of Eqs. 8, 9, 10 and 11 allows to calculate the fraction or
percentage of drug present in each of the compartments
(VH, ocular tissues, and systemic) as well as the total
fraction or percentage of drug eliminated by the organism
at any moment in time (Fig. 7). These simulations suggest
that the fraction of drug present in the ocular tissues
compartment is highest * 29 h post-administration,
reaching * 20% of the total administered dose. By con-
trast, the percentage of drug present in the systemic com-
partment is predicted to be low, remaining\ 2% of the
total administered drug at any point in time.
Total systemic exposure following intravenousand intravitreal administration
Total systemic exposure for intravenous or IVT adminis-
tration, represented by the area under the curve (AUC) for
the graph of plasma concentration vs. time, can be obtained
by integrating Eq. 4 or Eq. 13 between 0 and !, which is
straightforward for a sum of exponentials (Eq. 14).Z 1
0
Xi
i¼1Ai � e�ki�t ¼
Xi
i¼1
Ai
kið14Þ
Noteworthy, but not surprisingly, integration of Eq. 13,
i.e.Z 1
0
D � k1 � k2
VD;syst � k1 � k2ð Þ
� 1
k1 � k3
� e�k1�t þ 1
k3 � k2
� e�k2�t þ k1 � k2
k1 � k3ð Þ � k2 � k3ð Þ � e�k3�t
� �
ð15Þ
Fig. 6 General strategy for the analysis of drug plasma levels
following intravitreal administration. The mathematical model
(Eq. 13) is fed with data obtained from intravenous pharmacokinetics
(IV PK) and intravitreal pharmacokinetics (IVT PK) by attributing
fixed values to the parameters D, VD,syst, k1, and k3, leaving the sole
k2 as a variable parameter
Fig. 7 Percentage of drug present in each of the compartments (VH,
ocular tissues, and systemic) and total percentage of drug eliminated
following intravitreal administration of THR-149 in rabbit as
predicted based on the pharmacokinetic model depicted in Fig. 4b.
Calculations were based on Eqs. 8, 9, 10, 11 assuming the following
values for the individual rate constants: k1 = 0.0195 h-1;
k2 = 0.056 h-1; k3 = 0.64 h-1
0 24 48 72 96 120 144 168 192 216 2400.00
0.05
0.10
0.15
0.20
Time (h)
)Lm/gn(
noitartne cnoc941-RHT
Fig. 8 Plasma levels following intravitreal administration of 125 lg
of THR-149 in human as predicted by the pharmacokinetic model
shown in Fig. 4b and represented by Eq. 13. Parameters used for the
calculations were as follows: body weight = 70 kg; volume of
distribution = 36 L (0.51 L/kg); k1 = 0.014 h-1; k2 = 0.056 h-1;
k3 = 0.20 h-1
Journal of Pharmacokinetics and Pharmacodynamics (2021) 48:825–836 831
123
leads to
AUC0�1 ¼ D � k1 � k2
VD;syst � k1 � k2ð Þ
� 1
k1 � k1 � k3ð Þ þ1
k2 � k3 � k2ð Þ þk1 � k2
k3 � k1 � k3ð Þ � k2 � k3ð Þ
� �
ð16Þ
an expression which is identical to the solution obtained by
integrating Eq. 4:Z 1
0
D
VD;syst� e�k3�t ¼ D
k3 � VD;syst¼ D
CLsystð17Þ
This demonstrates that total systemic exposure is inde-
pendent of the route of administration and depends only on
the dose, the systemic volume of distribution, and the rate
constant of systemic elimination or, alternatively, on the
dose and the systemic clearance.
Extrapolation to human
Proper interpretation of pharmacokinetic data in preclinical
models is also essential to extrapolate or predict pharma-
cokinetics in human. Here, the predicted clearance of THR-
149 in the human VH can be determined using Eq. 18
(where the clearance is expressed in mL/h) which is based
on the experimental comparison of the vitreal clearance in
the rabbit and the human eye of a large number of com-
pounds [25]. The vitreal volume of distribution of THR-
149 in the human eye can be determined assuming that the
ratio between the volume of distribution and the volume of
vitreous is the same in the rabbit and in the human eye
(Eq. 19). Based on this and on Eq. 3, one can predict a
value of 0.014 h-1 (corresponding to a half-life of 51 h) for
the rate of elimination of THR-149 in the human VH (k1 in
model from Fig. 4b).
CLhuman ¼ 1:41 � CLrabbit þ 0:04 ð18ÞVolume of distribution humanð Þ
Vitreous volume humanð Þ 4:36 mL½ �¼ Volume of distribution rabbitð Þ 1:66 mL½ �
Vitreous volume rabbitð Þ 1:15 mL½ � ð19Þ
The rate of systemic elimination of THR-149 in human
(k3 in model from Fig. 4b) can be estimated assuming renal
clearance at glomerular filtration rate (120 mL/min for a
70 kg individual) and a systemic volume of distribution
identical to the one measured in the rabbit, i.e. 0.51 L/kg.
Using Eq. 6 one can then calculate a value of k3 of
0.20 h-1.
Based on the above numbers, it is thus possible to pre-
dict THR-149 plasma levels in human following IVT
administration using Eq. 13. The only unknown is the
value of the first-order rate constant for the elimination of
the drug from the ocular tissues compartment (k2 in model
from Fig. 4b) in humans. Depending on the availability of
specific information, it might be relevant to extrapolate the
value of k2 in human based e.g. on the difference in tra-
becular mesh outflow or retinal blood flow between the two
species. In the present case, though, there is no evidence
that k2 represents aqueous humor (AH)-to-plasma transfer
since AH-to-plasma transfer rate constants have been
reported either for small molecules or biologics that are
significantly larger than our value of k2 [17, 18]. Extrap-
olation of k2 to human based on trabecular mesh outflow
thus doesn’t seem appropriate. Similarly, since THR-149
elimination via the posterior route appears limited (see
discussion section), extrapolation of k2 to human based on
retinal blood flow seems equally inappropriate. In the
absence of a solid rationale to extrapolate that rate constant
from the data collected in rabbit, we thus chose to attribute
the same value of k2 in the two species. Predicted plasma
levels following monolateral IVT administration of 125 lg
of THR-149 (the highest dose tested in the clinic) are
shown in Fig. 8. Plasma concentration is expected to reach
a maximum value of only 0.15 ng/mL 39 h post-adminis-
tration before decaying slowly. Predicted total systemic
exposure is calculated to be 17.5 (ng/mL) h based on
Eq. 16.
Discussion
Bicyclic peptides are constrained peptides consisting of a
peptide sequence containing 3 cysteine residues which are
covalently linked to a thiol-reactive molecular scaffold
[26, 27]. With a molecular weight of * 1.7 kDa, THR-149
thus lies between conventional small molecule drugs and
macromolecules/biologics. At 0.032 mL/h, the vitreal
clearance of THR-149 in the rabbit eye is relatively low,
being at the very low end of the vitreal clearance spectrum
observed for small molecules and at the higher end of the
vitreal clearance spectrum observed for macromolecules,
which may indicate dominant drug elimination via the
anterior route and limited drug elimination via the posterior
route (blood-retinal barrier) [25, 28]. The vitreal volume of
distribution following IVT administration in rabbit was
found to be well within the narrow range of 0.72–3.6 mL
reported for a variety of molecules [25]. By contrast, with a
half-life of only 1.1 h, systemic elimination of THR-149 in
the rabbit is fast. The volume of distribution (0.51 L/kg)
suggests distribution in total body water. Systemic clear-
ance of THR-149 is 5.5 mL/min/kg which aligns with
systemic pharmacokinetics in the rat (not shown) and is
consistent with renal clearance [29].
Several approaches have been used to describe drug
circulating levels following IVT administration. Some of
832 Journal of Pharmacokinetics and Pharmacodynamics (2021) 48:825–836
123
the proposed models, however, are highly specific and/or
elaborated and their complexity requires the use of specific
software such as NONMEM (ICON Development Solu-
tions, Dublin, Ireland) or SimBiology (MathWorks, Inc.,
Natick, MA, USA). Therefore, by its simplicity, a two-
compartment model such as proposed by Xu et al. and
Zhang et al. [20, 21] (Fig. 4a) may arguably appear as the
most generally applicable. This model, however, proved
inadequate to describe THR-149 circulating levels fol-
lowing IVT administration in the rabbit. By contrast,
experimental data could be accurately represented on the
basis of a three-compartment model that assumes the
existence of an additional compartment localized between
the VH compartment and the systemic compartment
(Fig. 4b). Here, we have referred to the additional com-
partment as the ‘‘ocular tissues’’ compartment. Worth
noting, however, and because of the very nature of com-
partmental pharmacokinetic modelling, we cannot specu-
late as to where the drug exactly physically distributes in
that compartment; hence the model only provides infor-
mation on the drug distribution between the different
compartments over time as well as on the rates of drug
transfer from one compartment to the next.
Intuitively, because the vitreous is not in direct physical
contact with the plasma, the need to consider the existence
of an ocular tissues compartment to accurately describe the
evolution of plasma levels following IVT administration is
not incongruous. In addition, we report in our accompa-
nying paper a similar observation in the rabbit and the pig
for THR-687, a pan-integrin antagonist currently in
development for the treatment of diabetic macular edema.
We, therefore, hypothesize that the reasoning used here
applies to a majority of drugs administered intravitreally
and that circulating levels could be analyzed with the
model proposed here, at least for drugs which systemic
elimination obeys mono-compartmental pharmacokinetics
(for drugs which systemic elimination obeys bi-compart-
mental pharmacokinetics, we refer the reader to our
accompanying paper).
Another significant advantage of the methodology
depicted here lies in the fact that we provide an analytical
solution to the system of linear differential equations that
describes the proposed model, which eliminates the need
for complex software’s such as those mentioned above and
allows data analysis by standard nonlinear regression
analysis. Of note, it is conceivable that data analysis using
Eq. 13 would return a value of k2 much larger than the one
of k1. This, however, would not invalidate the general
concept proposed here but rather simply indicate that the
tested drug doesn’t accumulate significantly in the ocular
tissues compartment. To be observed, Eq. 13 simplifies
into Eq. 7 when k2 � k1 & k3.
Although accurately describing THR-149 circulating
levels following intravitreal administration, it is, however,
necessary to mention that one aspect that the proposed
model does not incorporate is binding to the drug target.
Drug-target interaction can potentially modify the overall
drug elimination and other researchers have very elegantly
addressed the matter (see e.g. [16, 17]). However, the
impact of target binding on overall drug elimination can
only become significant when the drug levels and the target
concentration are of the same order of magnitude. Given
that intravitreal administration results in high drug levels in
the vitreous chamber [2], it is likely that in a majority of
cases the drug concentration will be much larger than the
target concentration, making it possible to neglect drug-
target interaction in pharmacokinetic modelling.
Also, rather than the empirical approach used here
which assumes the existence of a unique and undefined
ocular tissues compartment, other pharmacokinetic models
have been proposed that incorporate more physiologi-
cal/morphological aspects of drug ocular elimination and
distribution. E.g. Gadkar et al., (2015), Le et al., (2015),
and Luu et al., (2020) have reported sophisticated models
that account for drug distribution within the retina (or
retina and choroid) and diffusion to the aqueous humor
[16, 17, 19], and Buitrago et al. have applied a model
which allows the drug to reach the circulation both from
the vitreous and from the aqueous humor, thereby
accounting for anterior and posterior ocular clearance [18].
However, given the differences in structure and assump-
tions made between our proposition and these different
models, additional studies applied to various types of drugs
will be necessary to compare these models for their ability
to accurately predict drug circulating levels following
ocular administration.
Conclusion
We describe, here and in our accompanying paper, phar-
macokinetic models for the analysis and prediction of
plasma levels following IVT administration and hypothe-
size that these models will apply to a variety of drugs
administered in the eye.
Appendix
We propose the following methodology to solve/integrate
Eq. syst. A.
Journal of Pharmacokinetics and Pharmacodynamics (2021) 48:825–836 833
123
dA=dt ¼ �k1 � AdB=dt ¼ k1 � A� k2 � BdC=dt
dD=dt
¼¼
k2 � B� k3 � Ck3 � C
ðsyst:AÞ
The first step is to re-arrange the system of differential
equations in the form of Eq. A:
dA=dtdB=dtdC=dtdD=dt
0
BB@
1
CCA ¼
�k1
k1
0
0
0
�k2
k2
0
0
0
�k3
k3
0
0
0
0
0
BB@
1
CCA
ABCD
0
BB@
1
CCA ðAÞ
Let’s call it the primary system and let’s call X the
column vector of the unknowns.
X ¼
ABCD
0
BB@
1
CCA ðBÞ
and
_X ¼
dA=dtdB=dtdC=dtdD=dt
0
BB@
1
CCA ðCÞ
its temporal derivative. Let’s also call
S ¼
�k1
k1
0
0
0
�k2
k2
0
0
0
�k3
k3
0
0
0
0
0
BB@
1
CCA ðDÞ
the primary system matrix. The primary system of differ-
ential equations can then be written in matrix form:
_X ¼ S � X ðEÞ
The four differential equations of the primary system
(Eq. syst. A) are coupled. This means that the derivative of
one unknown depends on one or several other unknowns.
For example, dB/dt depends on B with the coefficient - k2
but also on A with the coefficient k1. The reasoning here is
to de-couple the four equations so that the derivative of
each unknown only depends on itself. The mathematical
technique we used is the diagonalization of the matrix S so
that we can write:
S ¼ PDP�1 ðFÞ
where D is a diagonal matrix containing the eigenvalues of
the matrix S, i.e.:
D ¼
k1
0
0
0
0
k2
0
0
0
0
k3
0
0
0
0
k4
0
BB@
1
CCA ðGÞ
and P is a squared matrix where the columns are the
eigenvectors of S corresponding to the eigenvalues k1, k2,
k3, and k4, in the same order. P-1 is the inverse matrix of P.
The eigenvalues of the matrix S are the four solutions
(roots) of the characteristic equation of S:
dtm S� kIð Þ ¼ 0 ðHÞ
where dtm is the determinant of the matrix and I the
identity matrix. Here, k1 = - k1, k2 = - k2, k3 = - k3,
and k4 = 0 so that
D ¼
�k1
0
0
0
0
�k2
0
0
0
0
�k3
0
0
0
0
0
0
BB@
1
CCA ðIÞ
The eigenvectors vi associated to each eigenvalue ki
(i = 1, 2, 3, 4) are the solutions of the system
Svi ¼ kivi i ¼ 1; 2; 3; 4ð Þ ðJÞ
In our context, this leads to:
v1 ¼
� k1 � k2ð Þ k1 � k3ð Þ= k2k3ð Þk1 k1 � k3ð Þ= k2k3ð Þ
�k1=k3
1
0
BB@
1
CCA; v2
¼
0
k2 � k3ð Þ=k3
�k2=k3
1
0
BB@
1
CCA; v3 ¼
0
0
�1
1
0
BB@
1
CCA; v4 ¼
0
0
0
1
0
BB@
1
CCA ðKÞ
so that
P ¼
� k1 � k2ð Þ k1 � k3ð Þ= k2k3ð Þ 0 0 0
k1 k1 � k3ð Þ= k2k3ð Þ k2 � k3ð Þ=k3 0 0
�k1=k3 �k2=k3 �1 0
1 1 1 1
0
BB@
1
CCA
ðLÞ
To be noted, P only exists if k2.k3 = 0 and P-1 only
exists if k1 = k2, k1 = k3, and k2 = k3. If k1 = k2 and/or
k1 = k3 and/or k2 = k3, the matrix S is not diagonalizable
and the methodology described here is not applicable.
Including Eq. F into Eq. E leads to
_X ¼ PDP�1X ðMÞ
Multiplying the two sides of this last equality by P-1
leads to:
834 Journal of Pharmacokinetics and Pharmacodynamics (2021) 48:825–836
123
P�1 _X ¼ P�1PDP�1X $ _P�1X� �
¼ D P�1X� �
$ _Y ¼ DY
ðNÞ
where _P�1X� �
is equal to P�1 _X� �
since P-1 is a constant
matrix and where we introduced
Y ¼ P�1X ¼
A’
B’
C’
D’
0
BB@
1
CCA ðOÞ
Here, A0, B0, C0, and D0 are the four secondary
unknowns from which one can deduce the four primary
unknowns A, B, C, and D using
ABCD
0
BB@
1
CCA ¼ X ¼ PY ¼ P
A’
B’
C’
D’
0
BB@
1
CCA ðPÞ
The secondary system of differential equations
_Y ¼ DY ðQÞ
which can also be written
dA0=dtdB0=dtdC0=dtdD0=dt
0
BB@
1
CCA ¼
k1
0
0
0
0
k2
0
0
0
0
k3
0
0
0
0
k4
0
BB@
1
CCA
A0
B0
C0
D0
0
BB@
1
CCA ðRÞ
is now de-coupled and each of the four secondary differ-
ential equations can be solved/integrated separately with:
A0 ¼ C1 � ek1�t ¼ C1 � e�k1�t
B0 ¼ C2 � ek2�t ¼ C2 � e�k2�t
C0 ¼ C3 � ek3�t ¼ C3 � e�k3�t
D0 ¼ C4 � ek4�t ¼ C4
ðsyst:BÞ
where C1, C2, C3, and C4 are constants that will be fixed
based on the initial conditions of the primary system.
Introducing A0, B0, C0, and D0 in Eq. P and using Eq. L of
matrix P leads to:
A
B
C
D
0
BBB@
1
CCCA¼
� k1 � k2ð Þ k1 � k3ð Þ= k2k3ð Þ 0 0 0
k1 k1 � k3ð Þ= k2k3ð Þ k2 � k3ð Þ=k3 0 0
�k1=k3 �k2=k3 �1 0
1 1 1 1
0
BBB@
1
CCCA
C1 � e�k1�t
C2 � e�k2�t
C3 � e�k3�t
C4
0
BBB@
1
CCCA
ðSÞ
or
At ¼ �C1 �k1 � k2ð Þ k1 � k3ð Þ
k2k3
� e�k1�t
Bt ¼ C1 �k1 k1 � k3ð Þ
k2k3
� e�k1�t þ C2 �k2 � k3
k3
� e�k2�t
Ct
Dt
¼
¼
�C1 �k1
k3
� e�k1�t � C2 �k2
k3
� e�k2�t � C3 � e�k3�t
C1 � e�k1�t þ C2 � e�k2�t þ C3 � e�k3�t þ C4
ðsyst:CÞ
Using as initial conditions At=0 = A0, Bt=0 = 0, Ct=0
= 0, and Dt=0 = 0 leads to a linear system of four equations
in the four scalar unknowns C1, C2, C3, and C4 the reso-
lution of which leads to:
C1 ¼ A0 �k2 � k3
k2 � k1ð Þ � k1 � k3ð Þ ðTÞ
C2 ¼ A0 �k1 � k3
k1 � k2ð Þ � k2 � k3ð Þ ðUÞ
C3 ¼ A0 �k1 � k2 � k2 � k1ð Þ
k1 � k2ð Þ � k1 � k3ð Þ � k2 � k3ð Þ ðVÞ
C4¼A0 �k2 �k3 � k2�k3ð Þ�k1 �k3 � k1�k3ð Þþk1 �k2 � k1�k2ð Þ
k1�k2ð Þ� k1�k3ð Þ� k2�k3ð ÞðWÞ
Finally, introducing Eqs. T, U, V and W into Eq. syst. C
and re-arranging leads to Eqs. 8, 9, 10 and 11 above.
Acknowledgements The authors wish to thank Astrid De Vriese, Nele
Leenders and Sofie Molenberghs (Oxurion N.V.) for excellent tech-
nical assistance, and Dr Jean H. M. Feyen for constant support.
Author contributions Experimental design & generation of experi-
mental data [BN, TVB]; Conceptualization [MV]; Mathematical
developments [MV, J-MW]; Data analysis & interpretation [MV];
Resources management [PB]; Writing of original draft manuscript
[MV]; Final review and editing of manuscript [PB, AS].
Declarations
Conflict of interest Jean-Marc Wagner has no financial or non-fi-
nancial interests to disclose. Marc Vanhove, Bernard Noppen, Tine
Van Bergen, and Philippe Barbeaux are employees of Oxurion N.V.
Alan Stitt is consultant to Oxurion N.V.
Open Access This article is licensed under a Creative Commons
Attribution 4.0 International License, which permits use, sharing,
adaptation, distribution and reproduction in any medium or format, as
long as you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons licence, and indicate
if changes were made. The images or other third party material in this
article are included in the article’s Creative Commons licence, unless
indicated otherwise in a credit line to the material. If material is not
included in the article’s Creative Commons licence and your intended
use is not permitted by statutory regulation or exceeds the permitted
use, you will need to obtain permission directly from the copyright
holder. To view a copy of this licence, visit http://creativecommons.
org/licenses/by/4.0/.
Journal of Pharmacokinetics and Pharmacodynamics (2021) 48:825–836 835
123
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